Finite Group Databasebeta

C3×#10601441 #14314588

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×#10601441

Splittings

HallC3×C5 ⋊ #2158
SylowC5 ⋊ C3×#2158

Subgroups

subgroupG/H
centerC2×C3×C4#686
commutatorC5×C8C22×C3×C4
FrattiniC2×C8C22×C3×D5
FittingC3×C5×#427C2
socleC22×C3×C5C2×D8
prime radicalC23×C3×C5D8
cosocleC2×C5×C8C23×C3
hypercenterC3×#427D5
hypocenterC5C3×#2158
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C3×#427

304 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 40286);